International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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A Balanced Model Reduction for Fuzzy Systems with Time Varying Delay

  • Published : 2004.06.01
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Abstract

This paper deals with a balanced model reduction for T-S(Takagi-Sugeno) fuzzy systems with time varying state delay. We define a generalized controllability gramian and a generalized observability gramian for a stable T-S fuzzy delayed systems. We obtain a balanced state space realization using the generalized controllability and observability gramian and obtain a reduced model by truncating states from the balanced state space realization. We also present an upper bound of the approximation error. The generalized controllability gramian and observability gramian can be computed from solutions of linear matrix inequalities. We demonstrate the efficacy of the suggested method by illustrating a numerical example.

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References

  1. B. C. Moore, 'Principal component analysis in linear systems: Controllability, observability and model reduction,' IEEE Trans. Automatic Contr., vol.26, pp.17-32, 1981 https://doi.org/10.1109/TAC.1981.1102568
  2. L. Pemebo and L. M. Silverman, 'Model reduction via balanced state space representations,' IEEE Trans. Automatic Contr., vol.27, pp.382-387, 1982 https://doi.org/10.1109/TAC.1982.1102945
  3. K. Glover, 'All optimal Hankel-nonn approximations of linear multivariable systems and their L$\infty$ error bounds,' Int. J. Control, vol.39, pp.1115-1193, 1984 https://doi.org/10.1080/00207178408933239
  4. Y. Liu and B. D. O. Anderson, 'Singular perturbation approximation of balanced systems,' Int. J. Control, vol.50, pp.1379-1405, 1989 https://doi.org/10.1080/00207178908953437
  5. G. D. Wood, P. J. Goddard and K. Glover, 'Approximation of linear parameter varying systems,' Proceedings of the 35th CDC, pp.406-411, Kobe, Japan, Dec. 1996
  6. C. L. Beck, J. Doyle and K. Glover, 'Model reduction of multidimensional and uncertain systems,' IEEE Trans. Automatic Contr., vol.41, pp.1466-1477, 1996 https://doi.org/10.1109/9.539427
  7. K.R. Lee, J.H. Kim, E.T. Jeung and H.B. Park, 'Output Feedback Robust H$\infty$ Control of Uncertain Fuzzy Dynamic Systems with Time Varying Delay', IEEE. Trans. on Fuzzy Systems, vol.8, No.6, pp.657-664, December 2000 https://doi.org/10.1109/91.890325
  8. M.S. Mahmoud and N.F.Al-Muthairi,'Design of robust controllers for time delay systems', IEEE Trans. on Automatic Contr., vol.39, pp.995-999, May 1994 https://doi.org/10.1109/9.284878
  9. E.T. Jeung, J.H. Kim and H.B. Park,' H$\infty$ output feedback controller design for linear systems with time varying delayed states', IEEE Trans. Automatic Cantr., Vol.43, pp.971-974, July 1998 https://doi.org/10.1109/9.701103
  10. K. Tanaka, T.Ikeda, H.O.Wang, 'Robust stabilization of a class of uncertain nonlinear systems via fuzzy control : Quadratic stabilizability, H$\infty$ control theory, and linear matrix inequalities', IEEE Trans. Fuzzy Systems, vol.4, no.1, pp.l-13, Feb., 1996
  11. S.K.Nguang, P.Shi, H$\infty$ Fuzzy output feedback control design for nonlinear systems : an LM1 approach', IEEE Trans. Fuzzy Systems, vol. 11, no.3, pp.331-340, June 2003 https://doi.org/10.1109/TFUZZ.2003.812691
  12. B.S.Chen, C.S. Tseng and H.I. Uang, 'Mixed H$_ $/H$\infty$ fuzzy output feedback control design for. nonlinear dynamic systems : an LMl approach' , IEEE Trans. Fuzzy Systems, vol.8, no.3, pp.249-265, June 2000 https://doi.org/10.1109/91.855915
  13. H.D. Tuan, P. Apkarian, T. Narikiyo and Y. Yamamoto, 'Parameterized linear matrix inequality techniques in fuzzy control system design', IEEE Trans. Fuzzy Systems, vol.9, no.2, pp.324-332, April 2001 https://doi.org/10.1109/91.919253
  14. Z.X. Han, G. Feng, B.L. Walcott and J. Ma, 'Dynamic output feedback controller design for fuzzy systems', IEEE Trans. Systems, Man and Cybernetics, part B, vol.30, no.1, pp.204-210, Feb. 2000 https://doi.org/10.1109/3477.826962
  15. P. Korba, R. Babuska, H.B. Verbruggen and P.M. Frank, 'Fuzzy gain scheduling : Controller and observer design based on Lyapunov method and convex optimization', IEEE Trans. Fuzzy'Systems, vol.11, no.3, pp.285-298, June 2003 https://doi.org/10.1109/TFUZZ.2003.812680